A flight condition where an aircraft's direction of motion is not aligned with its longitudinal axis, causing the aircraft to "slip" sideways through the air.
A sideslip (or simply slip) is a situation that exists when an aircraft's longitudinal axis is not aligned with its direction of motion, causing the aircraft to slip sideways though the air (hence the term "sideslip"). The angle between the aircraft's direction of motion and its longitudinal axis is called the sideslip angle (designated beta, or β, for short); if β=0°, the aircraft is flying straight and true, while, at 90° β, an aircraft would be flying with its fuselage (if any) side-on to its direction of motion, and, at a β of 180°, our poor pilots would find themselves in a straight tailslide (most aircraft cannot maintain controlled flight under the latter two conditions, however).
A sideslip is generated by applying a force to yaw the aircraft in one direction or the other, and then holding the aircraft in this orientation relative to the oncoming airflow (for instance, by applying and holding rudder, or throttling up one engine to a higher power than the other and not throttling it back down). External yawing forces applied to the aircraft (for instance, sideways gusts of wind) will also tend to throw it into a sideslip; its ability to spontaneously recover from a sideslip and weathervane back into the oncoming airflow is known as directional stability, and is usually provided by a vertical-stabilizer (the main challenge with developing a flying-wing - which, by definition, lacks any sort of vertical tail - is to maintain adequate directional stability without a vertical stabilizer), or, occasionally, and much less efficiently, by careful use of airbrakes.
Flying in a sideslip generally results in an increase in drag, as the aircraft is now hitting the oncoming airflow obliquely rather than head-on, and, thus, presenting a larger cross-section to said air (this can be quite dangerous if a sideslip develops without the pilot noticing, especially during takeoff, but can be quite helpful when done deliberately [for instance, to perform a steep approach into an airport surrounded by mountains without building up a dangerously-high airspeed during the descent]).
An airplane with nonzero wing-sweep will exhibit a tendency to roll when placed in a sideslip, known as slip-roll coupling. If the wings are swept rearwards, as they are in most airplanes, the airplane will tend to roll in the direction of the trailing wing (so, for instance, if the airplane is slipping to the left, with its nose angled to the right of the oncoming airflow and its right wing further back than its left wing, it will want to roll to the right, and vice versa), while, for the tiny minority of airplanes with forward-swept wings, the airplane will roll towards the leading wing (so that, in the aforementioned situation with the airplane slipping to the left, with its nose to the right, its left wing leading, and its right wing trailing, it will try to roll to the left, and vice versa). This behaviour can be either desirable (as it allows the airplane to be rolled using the rudder or differential throttle control in the event of a partial or complete failure of the airplane's primary flight-controls), or undesirable (as it makes the airplane more susceptible to dutch-roll), depending on the circumstances.
Depending on the aircraft, a sideslip can also have various other effects on the aircraft's aerodynamics.
A skid is a special case of a sideslip in an uncoordinated turn, where an airplane is banked in one direction and its nose is pointed towards the inside of the turn (for instance, an airplane in a right bank and slipping to the left, with its nose even further to the right than its already-right-turning flightpath); this is quite dangerous, as the wing on the inside of the turn is moving much more slowly than the wing on the outside, such that, if the aircraft enters a stall, the inner, lower, slower wing will stall first, resulting in one or more spins. In contrast, a turning sideslip with wings level (known as a boat turn) or banked into the leading wing exhibits benign stall behaviour, although it is still considerably draggier and less efficient than a coordinated turn.